Pages and profiles are different. You didn't used to be able to have a profile box and a tab for one application, but Facebook recently changed this. Probably because they stated the profile boxes are going away.
Adding an application as a tab on a Profile has always been a bit problematic and convoluted. The user had to click on the "+" tab, and your app may or may not appear under the list and/or come up in the search. However, 2 weeks ago Facebook announced support for an "add as tab" button.
http://wiki.developers.facebook.com/index.php/Fb:add-profile-tab
Note that a user cannot add your application as a "profile box" until you have posted content to their profile (profile.setFBML) to be displayed in the box. The you can use the fb:add-section-button tag to display the "Add to Profile" button in your application. Box content is cached, so every time you want to update the content you need to post it to Facebook.
Adding an app as a tab to a Page has always been fairly easy. Go to the apps facebook page (not the app) and click on the "Add to My Page" link in the top left.